we know the smaller cone's height is 1/4 of 12, namely 3
Check the picture below.
since we know the radius and height of both cones, let's get the area of the larger one and subtract from it the area of the smaller one, what's leftover is the Frustum's area.
[tex]\stackrel{\textit{\Large Areas}}{\stackrel{\textit{larger cone}}{\cfrac{\pi (6)^2(12)}{3}}~~ -~~\stackrel{\textit{small cone}}{\cfrac{\pi (\frac{3}{2})^2(3)}{3}}}\implies 144\pi -\cfrac{9\pi }{4}\implies \cfrac{567\pi }{4}~~\approx~~445.32[/tex]
